1. The rule
Profit is shared in the ratio of capital × time. If the time is the same for everyone, share in the ratio of capitals only.
Profit ratio A : B = C₁T₁ : C₂T₂.
2. Types and how to handle each
| Situation | What to compute |
|---|---|
| Same time | Ratio of capitals |
| B joins after m months | A: C₁ × 12, B: C₂ × (12 − m) |
| Partner adds or withdraws money mid-year | Split into periods: C × t for each and add |
| Find capital or time | Set C₁T₁/C₂T₂ = given profit ratio |
| Working partner gets a salary or % first | Pay the salary first, then share the rest |
| Interest on capital | Pay interest first, then share the rest |
3. Solved examples
A ₹20,000, B ₹30,000, C ₹50,000 for a year; profit ₹15,000 → 2 : 3 : 5 → C gets ₹7,500.
(ASO 2025 type) A starts with ₹3,500; B joins after 5 months with ₹9,000. Profit ratio = 3,500 × 12 : 9,000 × 7 = 42,000 : 63,000 = 2 : 3.
A puts ₹8,000; after 4 months withdraws ₹2,000. B puts ₹6,000 for the year. A: 8,000 × 4 + 6,000 × 8 = 80,000; B: 72,000 → 10 : 9.
Capitals 3 : 4, profits 1 : 2, A's money for 8 months → 3 × 8 : 4t = 1 : 2 → t = 12 months.
A (working) gets 10% of ₹50,000 profit as salary = ₹5,000; ₹45,000 shared 2 : 3 → A gets 18,000 + 5,000 = ₹23,000.
4. Traps
- Always convert time to the same unit (months).
- "Joins after 3 months" in a 12-month year → 9 months of investment.
- Sleeping partner gets only the capital share.
Solved examples by question type
Each type that comes in the ASO paper, worked step by step. Try it yourself first, then read the solution.
Basic level
Example 1. A, B and C start a business with ₹15,000, ₹16,000 and ₹15,000. Out of an annual profit of ₹59,800, B's share is:
(a) ₹22,881 (b) ₹20,800 (c) ₹19,500 (d) ₹19,933
Answer: (b) ₹20,800
Solution: Ratio 15 : 16 : 15. B = 59,800 × 16/46 = ₹20,800.
Example 2. A, B and C start a business with ₹5,000, ₹9,000 and ₹11,000. Out of an annual profit of ₹5,000, B's share is:
(a) ₹1,666 (b) ₹2,200 (c) ₹1,000 (d) ₹1,800
Answer: (d) ₹1,800
Solution: Ratio 5 : 9 : 11. B = 5,000 × 9/25 = ₹1,800.
ASO exam level
Example 3. A starts a business with ₹4,000. After 4 months B joins with ₹6,000. At the end of the year, the profit is shared in the ratio:
(a) 1 : 1 (b) 2 : 1 (c) 2 : 3 (d) 8 : 12
Answer: (a) 1 : 1
Solution: A: 4,000×12 = 48,000. B: 6,000×8 = 48,000. Ratio = 1 : 1.
Example 4. A starts a business with ₹6,000. After 3 months B joins with ₹8,000. At the end of the year, the profit is shared in the ratio:
(a) 9 : 12 (b) 2 : 1 (c) 1 : 1 (d) 3 : 4
Answer: (c) 1 : 1
Solution: A: 6,000×12 = 72,000. B: 8,000×9 = 72,000. Ratio = 1 : 1.
Example 5. A starts a business with ₹3,500. After 5 months B joins as a partner. After a year, the profit is divided in the ratio 1 : 1. B's capital was:
(a) ₹3,000 (b) ₹3,500 (c) ₹7,000 (d) ₹6,000
Answer: (d) ₹6,000
Solution: 3,500×12 : B×7 = 1 : 1 → B = 3,500×12×1/(1×7) = ₹6,000.
Example 6. A, B and C invest in the ratio 3:4:5 for 12, 12 and 12 months respectively. Out of a profit of ₹36,000, C gets:
(a) ₹16,000 (b) ₹12,000 (c) ₹16,501 (d) ₹15,000
Answer: (d) ₹15,000
Solution: Capital × time: 36 : 48 : 60. C = 36,000 × 60/144 = ₹15,000.
Example 7. A starts a business with ₹15,000. B joins after 8 months with ₹8,000. Out of a yearly profit of ₹58,300, B gets:
(a) ₹8,900 (b) ₹49,500 (c) ₹9,900 (d) ₹8,800
Answer: (d) ₹8,800
Solution: A: 15,000×12 = 1,80,000; B: 8,000×4 = 32,000. Ratio 45 : 8. B = ₹8,800.
Example 8. A and B invest capitals in the ratio 9 : 1. The profits are in the ratio 12 : 1. If B's money was used for 9 months, A's money was used for:
(a) 13 months (b) 12 months (c) 9 months (d) 10 months
Answer: (b) 12 months
Solution: 9×tA : 1×9 = 12 : 1 → tA = 12 months.
Example 9. A, B and C share a profit in the ratio 1 : 2 : 2. If C gets ₹6,400, the total profit is:
(a) ₹17,601 (b) ₹9,600 (c) ₹16,000 (d) ₹19,200
Answer: (c) ₹16,000
Solution: One part = 6,400/2 = 3,200. Total = 5 × 3,200 = ₹16,000.
Advanced level
Example 10. A and B start a business with ₹12,000 and ₹12,000. After 3 months A withdraws ₹5,000. The profit at the end of the year is shared in the ratio:
(a) 7 : 12 (b) 11 : 16 (c) 1 : 1 (d) 16 : 11
Answer: (b) 11 : 16
Solution: A: 12,000×3 + 7,000×9 = 99,000. B: 12,000×12 = 1,44,000. Ratio 11 : 16.
Example 11. A and B start a business with ₹3,000 and ₹18,000. After 7 months A withdraws ₹2,000. The profit at the end of the year is shared in the ratio:
(a) 1 : 18 (b) 1 : 6 (c) 108 : 13 (d) 13 : 108
Answer: (d) 13 : 108
Solution: A: 3,000×7 + 1,000×5 = 26,000. B: 18,000×12 = 2,16,000. Ratio 13 : 108.
Example 12. A is a working partner and B a sleeping partner. A gets 20% of the profit for managing; the rest is shared in the ratio of capitals 6 : 5. If the total profit is ₹27,500, A receives:
(a) ₹15,000 (b) ₹17,600 (c) ₹17,500 (d) ₹12,000
Answer: (c) ₹17,500
Solution: Salary = 20% of 27,500 = ₹5,500. Rest ₹22,000 in 6 : 5 → A gets ₹12,000. Total = ₹17,500.
Example 13. A is a working partner and B a sleeping partner. A gets 20% of the profit for managing; the rest is shared in the ratio of capitals 5 : 6. If the total profit is ₹19,250, A receives:
(a) ₹7,000 (b) ₹10,950 (c) ₹10,850 (d) ₹8,750
Answer: (c) ₹10,850
Solution: Salary = 20% of 19,250 = ₹3,850. Rest ₹15,400 in 5 : 6 → A gets ₹7,000. Total = ₹10,850.
Topic-wise practice for Partnership (Quant): Profit sharing by capital and time. Useful for OPSC ASO, OSSC, OSSSC and other Odisha exams.
Question types covered
- Simple partnership (equal time)
- Compound partnership (different times)
- Partner joins or leaves midway
- Working partner's salary or share
- Finding capital or time from the profit share